// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_REF_H
#define EIGEN_REF_H

namespace Eigen {

namespace internal {

template<typename _PlainObjectType, int _Options, typename _StrideType>
struct traits<Ref<_PlainObjectType, _Options, _StrideType>>
	: public traits<Map<_PlainObjectType, _Options, _StrideType>>
{
	typedef _PlainObjectType PlainObjectType;
	typedef _StrideType StrideType;
	enum
	{
		Options = _Options,
		Flags = traits<Map<_PlainObjectType, _Options, _StrideType>>::Flags | NestByRefBit,
		Alignment = traits<Map<_PlainObjectType, _Options, _StrideType>>::Alignment
	};

	template<typename Derived>
	struct match
	{
		enum
		{
			IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime,
			HasDirectAccess = internal::has_direct_access<Derived>::ret,
			StorageOrderMatch =
				IsVectorAtCompileTime || ((PlainObjectType::Flags & RowMajorBit) == (Derived::Flags & RowMajorBit)),
			InnerStrideMatch =
				int(StrideType::InnerStrideAtCompileTime) == int(Dynamic) ||
				int(StrideType::InnerStrideAtCompileTime) == int(Derived::InnerStrideAtCompileTime) ||
				(int(StrideType::InnerStrideAtCompileTime) == 0 && int(Derived::InnerStrideAtCompileTime) == 1),
			OuterStrideMatch = IsVectorAtCompileTime || int(StrideType::OuterStrideAtCompileTime) == int(Dynamic) ||
							   int(StrideType::OuterStrideAtCompileTime) == int(Derived::OuterStrideAtCompileTime),
			// NOTE, this indirection of evaluator<Derived>::Alignment is needed
			// to workaround a very strange bug in MSVC related to the instantiation
			// of has_*ary_operator in evaluator<CwiseNullaryOp>.
			// This line is surprisingly very sensitive. For instance, simply adding parenthesis
			// as "DerivedAlignment = (int(evaluator<Derived>::Alignment))," will make MSVC fail...
			DerivedAlignment = int(evaluator<Derived>::Alignment),
			AlignmentMatch = (int(traits<PlainObjectType>::Alignment) == int(Unaligned)) ||
							 (DerivedAlignment >= int(Alignment)), // FIXME the first condition is not very clear, it
																   // should be replaced by the required alignment
			ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,
			MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch &&
								 AlignmentMatch && ScalarTypeMatch
		};
		typedef
			typename internal::conditional<MatchAtCompileTime, internal::true_type, internal::false_type>::type type;
	};
};

template<typename Derived>
struct traits<RefBase<Derived>> : public traits<Derived>
{};

}

template<typename Derived>
class RefBase : public MapBase<Derived>
{
	typedef typename internal::traits<Derived>::PlainObjectType PlainObjectType;
	typedef typename internal::traits<Derived>::StrideType StrideType;

  public:
	typedef MapBase<Derived> Base;
	EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const
	{
		return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const
	{
		return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
			   : IsVectorAtCompileTime					 ? this->size()
			   : int(Flags) & RowMajorBit				 ? this->cols()
														 : this->rows();
	}

	EIGEN_DEVICE_FUNC RefBase()
		: Base(0,
			   RowsAtCompileTime == Dynamic ? 0 : RowsAtCompileTime,
			   ColsAtCompileTime == Dynamic ? 0 : ColsAtCompileTime)
		,
		// Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values:
		m_stride(StrideType::OuterStrideAtCompileTime == Dynamic ? 0 : StrideType::OuterStrideAtCompileTime,
				 StrideType::InnerStrideAtCompileTime == Dynamic ? 0 : StrideType::InnerStrideAtCompileTime)
	{
	}

	EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase)

  protected:
	typedef Stride<StrideType::OuterStrideAtCompileTime, StrideType::InnerStrideAtCompileTime> StrideBase;

	// Resolves inner stride if default 0.
	static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveInnerStride(Index inner) { return inner == 0 ? 1 : inner; }

	// Resolves outer stride if default 0.
	static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index
	resolveOuterStride(Index inner, Index outer, Index rows, Index cols, bool isVectorAtCompileTime, bool isRowMajor)
	{
		return outer == 0 ? isVectorAtCompileTime ? inner * rows * cols
							: isRowMajor		  ? inner * cols
												  : inner * rows
						  : outer;
	}

	// Returns true if construction is valid, false if there is a stride mismatch,
	// and fails if there is a size mismatch.
	template<typename Expression>
	EIGEN_DEVICE_FUNC bool construct(Expression& expr)
	{
		// Check matrix sizes.  If this is a compile-time vector, we do allow
		// implicitly transposing.
		EIGEN_STATIC_ASSERT(EIGEN_PREDICATE_SAME_MATRIX_SIZE(PlainObjectType, Expression)
								// If it is a vector, the transpose sizes might match.
								|| (PlainObjectType::IsVectorAtCompileTime &&
									((int(PlainObjectType::RowsAtCompileTime) == Eigen::Dynamic ||
									  int(Expression::ColsAtCompileTime) == Eigen::Dynamic ||
									  int(PlainObjectType::RowsAtCompileTime) == int(Expression::ColsAtCompileTime)) &&
									 (int(PlainObjectType::ColsAtCompileTime) == Eigen::Dynamic ||
									  int(Expression::RowsAtCompileTime) == Eigen::Dynamic ||
									  int(PlainObjectType::ColsAtCompileTime) == int(Expression::RowsAtCompileTime)))),
							YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)

		// Determine runtime rows and columns.
		Index rows = expr.rows();
		Index cols = expr.cols();
		if (PlainObjectType::RowsAtCompileTime == 1) {
			eigen_assert(expr.rows() == 1 || expr.cols() == 1);
			rows = 1;
			cols = expr.size();
		} else if (PlainObjectType::ColsAtCompileTime == 1) {
			eigen_assert(expr.rows() == 1 || expr.cols() == 1);
			rows = expr.size();
			cols = 1;
		}
		// Verify that the sizes are valid.
		eigen_assert((PlainObjectType::RowsAtCompileTime == Dynamic) || (PlainObjectType::RowsAtCompileTime == rows));
		eigen_assert((PlainObjectType::ColsAtCompileTime == Dynamic) || (PlainObjectType::ColsAtCompileTime == cols));

		// If this is a vector, we might be transposing, which means that stride should swap.
		const bool transpose = PlainObjectType::IsVectorAtCompileTime && (rows != expr.rows());
		// If the storage format differs, we also need to swap the stride.
		const bool row_major = ((PlainObjectType::Flags)&RowMajorBit) != 0;
		const bool expr_row_major = (Expression::Flags & RowMajorBit) != 0;
		const bool storage_differs = (row_major != expr_row_major);

		const bool swap_stride = (transpose != storage_differs);

		// Determine expr's actual strides, resolving any defaults if zero.
		const Index expr_inner_actual = resolveInnerStride(expr.innerStride());
		const Index expr_outer_actual = resolveOuterStride(expr_inner_actual,
														   expr.outerStride(),
														   expr.rows(),
														   expr.cols(),
														   Expression::IsVectorAtCompileTime != 0,
														   expr_row_major);

		// If this is a column-major row vector or row-major column vector, the inner-stride
		// is arbitrary, so set it to either the compile-time inner stride or 1.
		const bool row_vector = (rows == 1);
		const bool col_vector = (cols == 1);
		const Index inner_stride =
			((!row_major && row_vector) || (row_major && col_vector))
				? (StrideType::InnerStrideAtCompileTime > 0 ? Index(StrideType::InnerStrideAtCompileTime) : 1)
			: swap_stride ? expr_outer_actual
						  : expr_inner_actual;

		// If this is a column-major column vector or row-major row vector, the outer-stride
		// is arbitrary, so set it to either the compile-time outer stride or vector size.
		const Index outer_stride =
			((!row_major && col_vector) || (row_major && row_vector))
				? (StrideType::OuterStrideAtCompileTime > 0 ? Index(StrideType::OuterStrideAtCompileTime)
															: rows * cols * inner_stride)
			: swap_stride ? expr_inner_actual
						  : expr_outer_actual;

		// Check if given inner/outer strides are compatible with compile-time strides.
		const bool inner_valid = (StrideType::InnerStrideAtCompileTime == Dynamic) ||
								 (resolveInnerStride(Index(StrideType::InnerStrideAtCompileTime)) == inner_stride);
		if (!inner_valid) {
			return false;
		}

		const bool outer_valid = (StrideType::OuterStrideAtCompileTime == Dynamic) ||
								 (resolveOuterStride(inner_stride,
													 Index(StrideType::OuterStrideAtCompileTime),
													 rows,
													 cols,
													 PlainObjectType::IsVectorAtCompileTime != 0,
													 row_major) == outer_stride);
		if (!outer_valid) {
			return false;
		}

		::new (static_cast<Base*>(this)) Base(expr.data(), rows, cols);
		::new (&m_stride) StrideBase((StrideType::OuterStrideAtCompileTime == 0) ? 0 : outer_stride,
									 (StrideType::InnerStrideAtCompileTime == 0) ? 0 : inner_stride);
		return true;
	}

	StrideBase m_stride;
};

/** \class Ref
 * \ingroup Core_Module
 *
 * \brief A matrix or vector expression mapping an existing expression
 *
 * \tparam PlainObjectType the equivalent matrix type of the mapped data
 * \tparam Options specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32,
 * \c #Aligned16, \c #Aligned8 or \c #Unaligned. The default is \c #Unaligned. \tparam StrideType optionally specifies
 * strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1), but accepts a
 * variable outer stride (leading dimension). This can be overridden by specifying strides. The type passed here must be
 * a specialization of the Stride template, see examples below.
 *
 * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the
 * number of copies. A Ref<> object can represent either a const expression or a l-value: \code
 * // in-out argument:
 * void foo1(Ref<VectorXf> x);
 *
 * // read-only const argument:
 * void foo2(const Ref<const VectorXf>& x);
 * \endcode
 *
 * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation
 * issue will be triggered. By default, a Ref<VectorXf> can reference any dense vector expression of float having a
 * contiguous memory layout. Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float
 * whose column's elements are contiguously stored with the possibility to have a constant space in-between each column,
 * i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension) can be greater than the number
 * of rows.
 *
 * In the const case, if the input expression does not match the above requirement, then it is evaluated into a
 * temporary before being passed to the function. Here are some examples: \code MatrixXf A; VectorXf a; foo1(a.head());
 * // OK foo1(A.col());              // OK foo1(A.row());              // Compilation error because here innerstride!=1
 * foo2(A.row());              // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object
 * foo2(A.row().transpose());  // The row is copied into a contiguous temporary
 * foo2(2*a);                  // The expression is evaluated into a temporary
 * foo2(A.col().segment(2,4)); // No temporary
 * \endcode
 *
 * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.
 * Here is an example accepting an innerstride!=1:
 * \code
 * // in-out argument:
 * void foo3(Ref<VectorXf,0,InnerStride<> > x);
 * foo3(A.row());              // OK
 * \endcode
 * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to
 * exploit vectorization, and will involve more expensive address computations even if the input is contiguously stored
 * in memory. To overcome this issue, one might propose to overload internally calling a template function, e.g.: \code
 * // in the .h:
 * void foo(const Ref<MatrixXf>& A);
 * void foo(const Ref<MatrixXf,0,Stride<> >& A);
 *
 * // in the .cpp:
 * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
 *     ... // crazy code goes here
 * }
 * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
 * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
 * \endcode
 *
 * See also the following stackoverflow questions for further references:
 *  - <a href="http://stackoverflow.com/questions/21132538/correct-usage-of-the-eigenref-class">Correct usage of the
 * Eigen::Ref<> class</a>
 *
 * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
 */
template<typename PlainObjectType, int Options, typename StrideType>
class Ref : public RefBase<Ref<PlainObjectType, Options, StrideType>>
{
  private:
	typedef internal::traits<Ref> Traits;
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline Ref(
		const PlainObjectBase<Derived>& expr,
		typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>::type* = 0);

  public:
	typedef RefBase<Ref> Base;
	EIGEN_DENSE_PUBLIC_INTERFACE(Ref)

#ifndef EIGEN_PARSED_BY_DOXYGEN
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline Ref(
		PlainObjectBase<Derived>& expr,
		typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>::type* = 0)
	{
		EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
		// Construction must pass since we will not create temprary storage in the non-const case.
		const bool success = Base::construct(expr.derived());
		EIGEN_UNUSED_VARIABLE(success)
		eigen_assert(success);
	}
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline Ref(
		const DenseBase<Derived>& expr,
		typename internal::enable_if<bool(Traits::template match<Derived>::MatchAtCompileTime), Derived>::type* = 0)
#else
	/** Implicit constructor from any dense expression */
	template<typename Derived>
	inline Ref(DenseBase<Derived>& expr)
#endif
	{
		EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value),
							THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
		EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
		EIGEN_STATIC_ASSERT(!Derived::IsPlainObjectBase, THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
		// Construction must pass since we will not create temporary storage in the non-const case.
		const bool success = Base::construct(expr.const_cast_derived());
		EIGEN_UNUSED_VARIABLE(success)
		eigen_assert(success);
	}

	EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref)
};

// this is the const ref version
template<typename TPlainObjectType, int Options, typename StrideType>
class Ref<const TPlainObjectType, Options, StrideType>
	: public RefBase<Ref<const TPlainObjectType, Options, StrideType>>
{
	typedef internal::traits<Ref> Traits;

  public:
	typedef RefBase<Ref> Base;
	EIGEN_DENSE_PUBLIC_INTERFACE(Ref)

	template<typename Derived>
	EIGEN_DEVICE_FUNC inline Ref(
		const DenseBase<Derived>& expr,
		typename internal::enable_if<bool(Traits::template match<Derived>::ScalarTypeMatch), Derived>::type* = 0)
	{
		//      std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch <<
		//      "," << match_helper<Derived>::InnerStrideMatch << "\n"; std::cout <<
		//      int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n";
		//      std::cout << int(StrideType::InnerStrideAtCompileTime) << " - " <<
		//      int(Derived::InnerStrideAtCompileTime) << "\n";
		construct(expr.derived(), typename Traits::template match<Derived>::type());
	}

	EIGEN_DEVICE_FUNC inline Ref(const Ref& other)
		: Base(other)
	{
		// copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
	}

	template<typename OtherRef>
	EIGEN_DEVICE_FUNC inline Ref(const RefBase<OtherRef>& other)
	{
		construct(other.derived(), typename Traits::template match<OtherRef>::type());
	}

  protected:
	template<typename Expression>
	EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::true_type)
	{
		// Check if we can use the underlying expr's storage directly, otherwise call the copy version.
		if (!Base::construct(expr)) {
			construct(expr, internal::false_type());
		}
	}

	template<typename Expression>
	EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type)
	{
		internal::call_assignment_no_alias(m_object, expr, internal::assign_op<Scalar, Scalar>());
		Base::construct(m_object);
	}

  protected:
	TPlainObjectType m_object;
};

} // end namespace Eigen

#endif // EIGEN_REF_H
